The meaning of a gift is what it says about the relationship between the people who are exchanging the gifts.
The material object serves as a vehicle to convey the esteem the parties have for each other. The point of gift exchange is to propel the personal relationship and to make sure nothing interrupts the to-and-fro of the minor reinforcement of each other's mutual esteem. Giving too valuable a gift can just as much injure the continuity of the relationship as either giving a gift that is too mean or in not reciprocating at all.
The claim, the purchase, the belonging people experience over the material objects in their possession becomes weaker as the belonging of the parties to each other becomes stronger.
Material interaction is actually comprised of a dual optimization: maximize the person-to-person belonging relative to the belonging of the objects to the persons; and then maximize the preference efficiencies subject to the belonging of the objects to the person. That dual optimization corresponds to (a) the prior decision about whether you want to do business with someone in the first place, and then (b) the follow-on decision about what the price and the terms of the deal need to be.
Gifts are the instruments of trust the way prices are the instruments of worth. Trust is a kind of belonging. It is a measure of the durability and stablity of the belonging relationship. As storage measures the durability and stability of the maintenance of value, so trust measures the durability and stability of the maintenance of a relationship.